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Sem 5 Prep
← OperationsThe economic production quantity

Formulas for this chapter

Maximum inventory (EPQ)

I_max = (Qp / p) x (p - u)

The first thing to compute once Qp is known. Read it as run length times net rate of build-up.

Qp
Run size (economic production quantity)
p
Production or delivery rate, per day
u
Usage rate, per day, in the same unit as p

Economic production quantity

Qp = sqrt( 2 D S / H ) x sqrt( p / (p - u) )

When the item is produced in batches while being used continuously, and p exceeds u.

D
Annual demand; derive it from the daily usage rate if needed
S
Setup cost per production run
H
Carrying cost per unit per year

Total cost (EPQ)

TC = (I_max / 2) H + (D / Q) S

Costing a production batch. Note I_max/2 rather than Q/2; the two halves are equal at the optimum.

I_max / 2
Average inventory over the cycle
(D / Q) S
Annual setup cost: runs a year times setup cost

Run time, cycle time, runs a year

Run time = Qp / p Cycle time = Qp / u Runs/year = D / Qp Idle time = cycle time - run time

Whenever a duration is asked for. Run time uses p; cycle time uses u.

p
Production rate per day
u
Usage rate per day
Step 2 of 19
The real wordsTheory

Why the batch case is different

The batch mode is widely used in production. In many cases the capacity to produce a part exceeds its usage or demand rate, so the firm produces for a while, stops, and lives off stock until the next run.

Economic production quantity (EPQ)The run size that minimises the sum of annual setup cost and annual carrying cost, when replenishment is gradual rather than instantaneous.

Two rate symbols do all the work: p, the production or delivery rate, and u, the usage rate. Both must be in the same time unit, usually per day.

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